The letter, which according to Financial Times reached the companies earlier in the week, has been sent to companies that deliver goods and services to the American state. The message is that they must follow the presidential order to continue doing business with the USA.
It is not clear how many or which companies have received the letter, which has been sent from American embassies around the EU, including in Paris.
The letter was first reported by the French newspaper Les Echos, and Financial Times refers to three unnamed sources. The British newspaper has also taken part in a questionnaire where European companies are expected to certify that they do not conduct any diversity programs.
France, which is already in a dispute with the USA over Trump's announced tariffs, is responding via its trade department:
"The American interference in the French companies' inclusion programs is unacceptable, as are the unjustified tariff threats", it says in a statement cited by the AFP news agency.